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Chapter 1: Q 96. (page 75)

ShakespeareThe histogram shows the distribution of lengths of words used in Shakespeare鈥檚 plays.

(a) Find the median word length in Shakespeare鈥檚 plays from the histogram. Explain your method clearly.

(b) Calculate the mean of the distribution. Show your work.

Short Answer

Expert verified

Part (a) 4 words.

Part (b) 4.13 words

Step by step solution

01

Part (a) Step 1. Given information.

The given histogram is shown below with their frequency:

02

Part (a) Step 2. Find the median word length in Shakespeare’s plays from the histogram. 

As we know that median is the middle value of a data set. As the given set is even, the median will be the average of two middle values (50th and 51st) of this sorted data.

Because 5+17+22=44(sum frequencies first three bars) and 5+17+22+23=67(sum frequencies first four bars), the 50th and 51st data values are both equal to 4 in the histogram's third bar.

M=4+42=4

The median units are the same as the data values' units, so the median is 4 words.

03

Part (b) Step 1. Calculate the mean of the distribution.

Word Length (x)Frequency (f)fx
155
21734
32266
42392
51260
6742
7535
8432
9327
10220
Total100413

x炉=鈭�fxn=413100=4.13

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